Functiones et Approximatio Commentarii Mathematici

Representation of a rational number as a sum of ninth or higher odd powers

M.A Reynya

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In the present paper, we substantially generalize one of the results obtained in our earlier paper [RM]. We present a solution of a problem of Waring type: if $F(x_1, \dots ,x_N)$ is a~symmetric form of odd degree $n\ge 9$ in $N=16\cdot 2^{n-9}$ variables, then for any $q\in \mathbb{Q}$, $q\neq 0$, the equation $F(x_i)=q$ has rational parametric solutions, that depend on $n-8$ parameters.

Article information

Funct. Approx. Comment. Math., Volume 58, Number 1 (2018), 79-87.

First available in Project Euclid: 5 May 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11D72: Equations in many variables [See also 11P55]
Secondary: 11P05: Waring's problem and variants

Diophantine equations parametric solutions


Reynya, M.A. Representation of a rational number as a sum of ninth or higher odd powers. Funct. Approx. Comment. Math. 58 (2018), no. 1, 79--87. doi:10.7169/facm/1646.

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